SECOND LAW OF THERMODYNAMICS

171.] The amount of heat absorbed corresponding to a given increase of thermo-electric power, must depend on the temperature as well as on the amount of that increase. For consider a circuit consisting of two metals, nei- ther of which exhibits the Thomson effect. Such a circuit would be repre- sented in the thermo-electric diagram by the parallelogram AabB with hori- zontal and vertical sides. If the current flows in the direction AabB heat is absorbed in BA and generated on ab, and no reversible thermal effect oc- curs elsewhere.

Also the heat absorbed in BA exceeds that generated in ab by a quantity represented by the parallelogram BAab. Hence if we produce Aa and Bb and draw the vertical line αβ at such a distance that the heat absorbed at the junction AB is represented by the parallelogram BAαβ, the heat generated at the junction ab, which, as we have seen, is less than this by the parallelogram BAab, will be represented by the parallelogram abβα. The Peltier effect therefore is measured by the product of the increase of thermo-electric power in passing from the first metal to the second into the temperature reckoned from some point lower than any observed temperature, and is of the form (φ2 − φ1 )(t − t1 ), when the current flows from a metal in which the thermo-electric power is φ1 to a metal in which it is φ2 , and t is the thermometer reading, and t1 is a constant, the value of which can be ascertained only by experiment.

172.] Thus far we are led by the principle of the Conservation of Energy. It is a consequence, however, of the Second Law of Thermodynamics, that in all strictly reversible operations in which heat is transformed into work or work into heat, the amount of heat absorbed or emitted at the higher tem- perature is to that emitted or absorbed at the lower temperature as the higher temperature is to the lower temperature, both being reckoned from absolute zero of the thermodynamic scale. It follows that the line αβ must be drawn in the position corresponding to the absolute zero of the thermodynamic scale, and that the expression for the heat absorbed may be written (φ2 −φ1 )θ, where θ is the temperature reckoned from absolute zero. It is true that the thermo- electric operations cannot be made completely reversible, as the conduction of heat, which is an irreversible operation, is always going on, and cannot be prevented. We must therefore consider the application of the Second Law of Thermodynamics to the reversible part of the phenomena as a very probable conjecture consistent with other parts of the theory of heat, and verified ap- proximately by the measurements of the Peltier and Thomson effects by Le Roux.

173.] We are now able to express all the thermal and electromotive effects in terms of the areas in the thermo-electric diagram. Let Ii be the line for one metal, say iron, Cc that for another, say copper. Let T be the higher tem- perature and t the lower, and let O represent the position of absolute zero. Let the current flow in the direction CIic till one unit of electricity has passed. Then the heat absorbed at the hot junction will be represented by the area CIQR. This is the Peltier effect.

The heat absorbed in the iron is represented by IiP Q …Thomson effect. The heat generated in the cold junction, by icSP …Peltier effect. The heat absorbed in the copper, by cCRS…Thomson effect. The whole heat absorbed is therefore represented by CIiP Sc, and the heat generated by icSP, leaving CIic for the heat absorbed as the result of theENTROPY. 154 Fig. 39. whole operation. This heat is converted into the work done on the electric current.

174.] Entropy∗ , in Thermodynamics, is a quantity relating to a body such that its increase or diminution implies that heat has entered or left the body. The amount of heat which enters or leaves the body is measured by the prod- uct of the increase or diminution of entropy into the temperature at which it takes place.

In this treatise we have avoided making any assumption that electricity is a body or that it is not a body, and we must also avoid any statement which might suggest that, like a body, electricity may receive or emit heat. We may, however, without any such assumption, make use of the idea of entropy, introduced by Clausius and Rankine into the theory of heat, and extend it to certain thermo-electric phenomena, always remembering that en- tropy is not a thing but a mere instrument of scientific thought, by which we are enabled to express in a compact and convenient manner the conditions under which heat is emitted or absorbed. ∗ [Arts. 174-181 consist principally of a repetition of Arts. 167-173, but expressed in the language of the doctrine of Entropy. It was probably the intention of Professor Clerk Maxwell to insert them or some modification of them in place of the foregoing Articles, but it has been thought best not to alter the continuous MS., but simply to insert the separate Articles here as representing a slightly different method of applying the Second Law of Thermodynamics to thermo-electric phenomena.]ELECTRIC ENTROPY.

175.] When an electric current passes from one metal to another heat is emitted or absorbed at the junction of the metals. We shall therefore sup- pose that the electric entropy has diminished or increased when the electric- ity passes from the one metal to the other, the electric entropy being different according to the nature of the medium in which the electricity is, and being affected by its temperature, stress, strain, &c. It is only, however, during the motion of electricity that any thermo-electric phenomena are produced. 176.] It is proved in treatises on thermodynamics that in all reversible thermal operations, what is called the entropy of the system remains the same. (Maxwell’s Theory of Heat, 5th ed. p. 190.)

The entropy of a body is a quantity which when the body receives (or H emits) a quantity of heat, H, increases (or diminishes) by a quantity , where θ θ is the temperature reckoned on the thermodynamic scale. The entropy of a material system is the sum of the entropies of its parts. 177.] The thermal effects of electric currents are in part reversible and in part irreversible, but the reversible effects, such as those discovered by Peltier and Thomson, are always small compared with the irreversible effects—the frictional generation of heat and the diffusion of heat by conduction. Hence we cannot extend the demonstration of the theorem, which applies to com- pletely reversible thermal operations, to thermo-electric phenomena.

But, as Sir Wm. Thomson has pointed out, we have great reason to conjecture that the reversible portion of the thermo-electric effects are subject to the same condition as other reversible thermal operations. This conjecture has not hitherto been disproved by any experiments, and it may hereafter be ver- ified by careful electric and calorimetric measurements. In the meantime the consequences which flow from this conjecture may be conveniently described by an extension of the term entropy to electric phenomena. The term Electric Entropy, as we shall use it, corresponds to the term Thermo-electric Power, as defined by Sir W. Thomson in his fifth paper on the Dynamical Theory of Heat (Trans. R. S. E. 1st May, 1854; Art. 140, p. 151).